






# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings("""ignore""", category=UserWarning, module="""torch.optim.lr_scheduler""")


class     _a							:






  """simple docstring"""





  def __init__(  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase = True		,		_UpperCAmelCase = False			)      ->			str:
     UpperCamelCase_						=  scheduler
     UpperCamelCase_						=  optimizers if isinstance(_UpperCAmelCase		,		(list, tuple)			) else [optimizers]
     UpperCamelCase_						=  split_batches
     UpperCamelCase_						=  step_with_optimizer
     UpperCamelCase_						=  GradientState()




  def  _UpperCAmelCase  (  self		,		*_UpperCAmelCase		,		**_UpperCAmelCase			)      ->			List[Any]:
     if not self.step_with_optimizer:
        # No link between scheduler and optimizer -> just step
        self.scheduler.step(*_UpperCAmelCase		,		**_UpperCAmelCase			)
        return

     # Otherwise, first make sure the optimizer was stepped.
     if not self.gradient_state.sync_gradients:
        if self.gradient_state.adjust_scheduler:
           self.scheduler._step_count += 1
        return

     for opt in self.optimizers:
        if opt.step_was_skipped:
           return
     if self.split_batches:
        # Split batches -> the training dataloader batch size is not changed so one step per training step
        self.scheduler.step(*_UpperCAmelCase		,		**_UpperCAmelCase			)
     else:
        # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
        # num_processes steps per training step
        UpperCamelCase_						=  AcceleratorState().num_processes
        for _ in range(_UpperCAmelCase			):
           # Special case when using OneCycle and `drop_last` was not used
           if hasattr(self.scheduler		,		'total_steps'			):
              if self.scheduler._step_count <= self.scheduler.total_steps:
                 self.scheduler.step(*_UpperCAmelCase		,		**_UpperCAmelCase			)
           else:
              self.scheduler.step(*_UpperCAmelCase		,		**_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self			)      ->			List[Any]:
     return self.scheduler.get_last_lr()




  def  _UpperCAmelCase  (  self			)      ->			Union[str, Any]:
     return self.scheduler.state_dict()




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			List[str]:
     self.scheduler.load_state_dict(_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self			)      ->			List[Any]:
     return self.scheduler.get_lr()




  def  _UpperCAmelCase  (  self		,		*_UpperCAmelCase		,		**_UpperCAmelCase			)      ->			Optional[Any]:
     return self.scheduler.print_lr(*_UpperCAmelCase		,		**_UpperCAmelCase			)






def 			lowercase(	UpperCamelCase_ = 100       )		->	int:







 '''simple docstring'''
 UpperCamelCase			  =      n * (n + 1) * (2 * n + 1) / 6
 UpperCamelCase			  =      (n * (n + 1) / 2) ** 2
 return int(square_of_sum - sum_of_squares       )


if __name__ == "__main__":
     print(F'''{solution() = }''')
